document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1025281>Question 1025281</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Let f be the function defined by f(x) = 2x + e^x. If g(x) = f^-1(x) for all x and the point (0,1) is on the graph of f, what is the value of g'(1)?\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #640562 by </B><A HREF=/tutors/aboutme.mpl?userid=robertb><B>robertb(5830)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=robertb><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=robertb><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=640562\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> If y = f(x), then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=df%5E%28-1%29%28y%29%2Fdy+=+1%2F%28dy%2Fdx%29+=+1%2F%28df%280%29%2Fdx%29 ALIGN=MIDDLE  ALT=\"df%5E%28-1%29%28y%29%2Fdy+=+1%2F%28dy%2Fdx%29+=+1%2F%28df%280%29%2Fdx%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  (A statement of the inverse function theorem. f(x) is continuously differentiable at x = 0.)\r<BR>\n" );
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document.write( "Now <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29+=+2x+%2B+e%5Ex ALIGN=MIDDLE  ALT=\"f%28x%29+=+2x+%2B+e%5Ex\"   DISABLED_style= \"max-width:90%; height:auto;\" > ==> f'(x) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=df%28x%29%2Fdx+=+2+%2B+e%5Ex+ ALIGN=MIDDLE  ALT=\"df%28x%29%2Fdx+=+2+%2B+e%5Ex+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "==> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=df%5E%28-1%29%281%29%2Fdy+=+dg%281%29%2Fdy+=+1%2F%28df%280%29%2Fdx%29+=+1%2F%282+%2B+e%5E0%29+=+1%2F3 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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